Extension of the $\nu$-metric for stabilizable plants over $H^{\infty }$

Abstract

An abstract $\nu$-metric was introduced by Ball and Sasane, with a view towards extending the classical $\nu$-metric of Vinnicombe from the case of rational transfer functions to more general nonrational transfer function classes of infinite-dimensional linear control systems. In this short note, we give an important concrete special instance of the abstract $\nu$-metric, by verifying that all the assumptions demanded in the abstract set-up are satisfied when the ring of stable transfer functions is the Hardy algebra $H^{\infty }$. This settles the open question implicit in \cite{BalSas2}.

arXiv comment12 pages